A065800 Numbers k which, for some r, are r-digit maximizers of k/phi(k).

6, 30, 60, 90, 210, 420, 630, 840, 2310, 4620, 6930, 9240, 30030, 60060, 90090, 510510, 9699690, 19399380, 29099070, 38798760, 48498450, 58198140, 67897830, 77597520, 87297210, 96996900, 223092870, 446185740, 669278610, 892371480

Offset

1,1

Comments

I can show that for r > 1, the first r-digit term of the sequence is the smallest r-digit primorial, if it exists. It remains to investigate the first terms when existence fails. It is also not hard to see that for r > 1, the r-digit terms are in arithmetic progression with common difference equal to the smallest r-digit term. For example, 210, 420, 630, 840 are in arithmetic progression with common difference 210. Obviously the r-digit minimizer of k/phi(k) is the largest prime of k digits.

Links

Table of n, a(n) for n=1..30.

Sean A. Irvine, Java program (github).

Example

30/phi(30) = 15/4 is maximal for two-digit numbers.
210/phi(210) = 35/8 is maximal for three-digit numbers.

Crossrefs

Cf. A000010, A002110, A065657.

Sequence in context: A120734 A116360 A336219 * A181827 A263573 A145010

Adjacent sequences: A065797 A065798 A065799 * A065801 A065802 A065803

Keyword

nonn,more

Author

Joseph L. Pe, Dec 05 2001

Extensions

a(13)-a(15) corrected and a(16)-a(30) from Sean A. Irvine, Sep 15 2023

Status

approved